No. All CERN personnel, regardless of grade, are subject to national traffic laws. For example, should you incur any speeding tickets, you are expected to pay the fine(s).
Conduct on the road can reflect upon CERN’s reputation, especially where it concerns a car that is identifiable as belonging to CERN or to a CERN staff member. If you are entitled to a CD plate, you should understand that you are a role model and, if anything, try to go beyond minimum requirements.